Gromov-Witten/Pairs descendent correspondence for toric 3-folds

Abstract

We construct a fully equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds X. Our method uses geometric constraints on descendents, A_n surfaces, and the topological vertex. The rationality of the stable pairs descendent theory plays a crucial role in the definition of the correspondence. We prove our correspondence has a non-equivariant limit. As a result of the construction, we prove an explicit non-equivariant stationary descendent correspondence for X (conjectured previously by MNOP). Using descendent methods, we establish the relative GW/Pairs correspondence for X/D in several basic new log Calabi-Yau geometries. Among the consequences is a rationality constraint for non-equivariant descendent Gromov-Witten series for P^3.

83 pages, minor changes

References in corpus (1)

• Descendents on local curves: Stationary theory

Cited by in corpus (16)

• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Double ramification cycles with target varieties
• Stable pair invariants of local Calabi-Yau 4-folds
• Curve counting on elliptic Calabi-Yau threefolds via derived categories
• Cobordism invariants of the moduli space of stable pairs
• Stable pairs with descendents on local surfaces I: the vertical component
• Stable pair invariants of surfaces and Seiberg-Witten invariants
• Double nested Hilbert schemes and the local stable pairs theory of curves
• Virasoro conjecture for the stable pairs descendent theory of simply connected 3-folds (with applications to the Hilbert scheme of points of a surface)
• Gromov-Witten theory of $K3\times {\mathbb{P}}^1$ and quasi-Jacobi forms
• Virasoro constraints for stable pairs on toric 3-folds
• Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
• Modular forms from Noether-Lefschetz theory
• Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
• The orbifold DT/PT vertex correspondence
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions